Dynamic models with $p$ parameters are identified by $2p+1$ random features

What the math gives to ML

The paper gives a dimension-aware identification principle for noisy dynamical systems: a p-parameter model can be identified by matching only 2p+1 generic nonlinear measurements of short trajectory windows. Its concrete measurement family is a randomized Fourier map, with independently sampled Gaussian frequencies and uniform phases. This suggests a compact trajectory-matching objective or auxiliary loss for neural ODEs, state-space models, and world models, where a low-dimensional parameter head is trained against random Fourier statistics rather than full trajectory likelihood. The main transferable asset is not random features alone, which are established, but the proposed feature budget tied directly to the number of dynamic parameters under broad noise assumptions.